diff --git a/comb_spec_searcher/comb_spec_searcher.py b/comb_spec_searcher/comb_spec_searcher.py
index ec05ec275..8e36f8150 100644
--- a/comb_spec_searcher/comb_spec_searcher.py
+++ b/comb_spec_searcher/comb_spec_searcher.py
@@ -282,6 +282,14 @@ def add_rule(
         """
         for comb_class, child_label in zip(rule.children, end_labels):
             if not rule.possibly_empty:
+                if self.debug:
+                    if comb_class.is_empty():
+                        logger.debug(
+                            "SANITY CHECK FAILURE.\n"
+                            " The folowing combinatorial class "
+                            "is set not empty but is empty!\n%s",
+                            comb_class,
+                        )
                 self.classdb.set_empty(child_label, empty=False)
             if self.symmetries and child_label not in self.symmetry_expanded:
                 self._symmetry_expand(comb_class, child_label)
@@ -551,7 +559,7 @@ def _auto_search_rules(
             logger.debug("Searching for specification.")
             if self.has_specification():
                 logger.info("Specification detected.")
-                return self.ruledb.get_specification_rules(
+                return self._get_specification_rules(
                     smallest=smallest,
                     minimization_time_limit=0.01 * (time.time() - auto_search_start),
                 )
@@ -623,10 +631,15 @@ def get_specification(
         """
         if not self.ruledb.has_specification():
             raise SpecificationNotFound
-        kwargs = {
-            "minimization_time_limit": minimization_time_limit,
-            "smallest": smallest,
-        }
-        rules = self.ruledb.get_specification_rules(**kwargs)
+        rules = self._get_specification_rules(
+            smallest=smallest, minimization_time_limit=minimization_time_limit
+        )
         logger.info("Creating a specification.")
         return CombinatorialSpecification(self.start_class, rules)
+
+    def _get_specification_rules(
+        self, smallest: bool = False, minimization_time_limit: float = 10
+    ) -> Iterator[AbstractRule]:
+        return self.ruledb.get_specification_rules(
+            smallest=smallest, minimization_time_limit=minimization_time_limit
+        )
diff --git a/comb_spec_searcher/combinatorial_class.py b/comb_spec_searcher/combinatorial_class.py
index db8da0a7b..6c1bbc394 100644
--- a/comb_spec_searcher/combinatorial_class.py
+++ b/comb_spec_searcher/combinatorial_class.py
@@ -203,6 +203,25 @@ def minimum_size_of_object(self) -> int:
             "'minimum_size_of_object' must be implemented."
         )
 
+    def min_size(self) -> int:
+        """
+        This is only here for when you are using an is empty method which returns
+        False on sets which are empty. If you are using an is empty method which
+        is 100% accurate, you can ignore this method.
+
+        Return the minimum size of the objects in the combinatorial class.
+        This is the method used by the Cartesian product constructor.
+        For productivity reasons, you must at least return 1, if this should be
+        greater than 0.
+
+        By default, CartesianProductStrategy assumes that all children are
+        non-empty, and hence this check is redundant so it instead calls the
+        'minimum_size_of_object' method. But, if you overwrite the
+        CartesianProductStrategy to allow for some children to be empty, then
+        the rules are reversible only if all children are non-empty.
+        """
+        return self.minimum_size_of_object()
+
     def to_bytes(self) -> bytes:
         """Return a compressed version of the class in the form of a 'bytes'
         object. If you are having memory issues then implement this function
diff --git a/comb_spec_searcher/rule_db/forest.py b/comb_spec_searcher/rule_db/forest.py
index b4f8c19eb..3cb5ae34e 100644
--- a/comb_spec_searcher/rule_db/forest.py
+++ b/comb_spec_searcher/rule_db/forest.py
@@ -689,6 +689,15 @@ def _add_empty_rule(self, ends: Iterable[int], rule: AbstractRule) -> None:
         Add empty rule for the children of the rule if needed.
         """
         if not rule.possibly_empty:
+            if self.searcher.debug:
+                for child in rule.children:
+                    if child.is_empty():
+                        logger.debug(
+                            "SANITY CHECK FAILURE.\n"
+                            " The folowing combinatorial class "
+                            "assumed not empty but is empty!\n%s",
+                            child,
+                        )
             return
         for label, comb_class in zip(ends, rule.children):
             if label not in self._already_empty and self.classdb.is_empty(
diff --git a/comb_spec_searcher/strategies/constructor/cartesian.py b/comb_spec_searcher/strategies/constructor/cartesian.py
index 15d273fcc..2b8ef8207 100644
--- a/comb_spec_searcher/strategies/constructor/cartesian.py
+++ b/comb_spec_searcher/strategies/constructor/cartesian.py
@@ -74,12 +74,9 @@ def __init__(
         for k in parent.extra_parameters:
             self.minimum_sizes[k] = parent.get_minimum_value(k)
 
-        self.min_child_sizes = tuple(
-            {"n": child.minimum_size_of_object()} for child in children
-        )
+        self.min_child_sizes = tuple({"n": child.min_size()} for child in children)
         self.max_child_sizes = tuple(
-            {"n": child.minimum_size_of_object()} if child.is_atom() else {}
-            for child in children
+            {"n": child.min_size()} if child.is_atom() else {} for child in children
         )
         self.parent_parameters = ("n",) + parent.extra_parameters
 
@@ -397,7 +394,7 @@ def __init__(
         self._children_param_maps = CartesianProduct._build_children_param_map(
             parent, children, self.extra_parameters
         )
-        self._min_sizes = tuple(child.minimum_size_of_object() for child in children)
+        self._min_sizes = tuple(child.min_size() for child in children)
         self._max_sizes = tuple(
             child.minimum_size_of_object() if child.is_atom() else None
             for child in children